CN112651106A - Method and device for determining equidistant great circle route - Google Patents
Method and device for determining equidistant great circle route Download PDFInfo
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Abstract
The application belongs to the field of airplane route design, and relates to a method and a device for determining equidistant great circle routes. The method comprises the following steps: step S1, determining the longitude and latitude of the starting point and the ending point of the great circle route; step S2, calculating great circle route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram Luger projection; step S3, calculating the distance between the starting point and the end point under the plane coordinates of the great circle route; step S4, dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval, and calculating the plane coordinate of each interval point; and step S5, converting the plane coordinates of each interval point into longitude and latitude by using a back calculation formula of Gaussian-gram Luger projection. The problem that the projection of the traditional ink card support is seriously deviated from a great circle route in a high latitude area is solved, the route is closer to a real global great circle route, and the economic principle of remote navigation is met.
Description
Technical Field
The application belongs to the field of airplane route design, and particularly relates to a method and a device for determining equidistant great circle routes.
Background
The displayed position of the aircraft during long-distance navigation does not correspond to the flight path. The true earth is an ellipsoid, so in a strict sense, the equal altitude flight path between two points is not a straight line, but an arc of the same curvature as the earth's surface. The course displayed by the on-board display is a straight line between two waypoints, and has a large error with the actual flight course of the airplane.
Disclosure of Invention
In order to solve the technical problem, the application provides a method and a device for determining an equidistant big circular route, which are applied to the aspect of designing an optimal route for long-distance navigation of an airplane.
The first aspect of the application provides a method for determining equidistant great circle route, comprising:
step S1, determining the longitude and latitude of the starting point and the ending point of the great circle route;
step S2, calculating great circle route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram Luger projection;
step S3, calculating the distance between the starting point and the end point under the plane coordinates of the great circle route;
step S4, dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval, and calculating the plane coordinate of each interval point;
and step S5, converting the plane coordinates of each interval point into longitude and latitude by using a back calculation formula of Gaussian-gram Luger projection.
Preferably, the set interval is 40-60 km.
Preferably, the set interval is 50 km.
Preferably, the method further comprises the following steps:
and S6, forming a great circle route according to the plurality of longitudes and latitudes calculated in the step S5, and guiding the aircraft to navigate.
The second aspect of the present application provides an equidistant great circle route determining device, including:
the starting longitude and latitude determining module is used for determining the longitude and latitude of a starting point and an ending point of the great circle route;
the starting plane coordinate calculation module is used for calculating large circular route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram-Luger projection;
the distance calculation module is used for calculating the distance between a starting point and a terminal point under the plane coordinates of the great circle route;
the interval division module is used for dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval and calculating the plane coordinate of each interval point;
and the interval point longitude and latitude determining module is used for converting the plane coordinates of each interval point into the longitude and latitude by using a back calculation formula of Gaussian-Kruger projection.
Preferably, the set interval is 40-60 km.
Preferably, the set interval is 50 km.
Preferably, the method further comprises the following steps:
and the great circle route determining module is used for forming a great circle route according to the plurality of the longitudes and latitudes calculated by the interval point longitude and latitude determining module and guiding the aircraft to navigate.
The problem that the projection of the traditional ink card support is seriously deviated from a great circle route in a high latitude area is solved, the route is closer to a real global great circle route, and the economic principle of remote navigation is met. The method solves the problem that the calculation result is divergent when the calculation error is large and the starting point and the end point latitude are close in the existing method in the high latitude area, and is wider in applicability and changed in precision. The application range of the equidistant great circle route design is effectively expanded, and powerful technical support is provided for the design of the long-distance navigation route of the airplane.
Drawings
FIG. 1 is a flow chart of the method for determining equidistant great circle routes.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all embodiments of the present application. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application, and should not be construed as limiting the present application. All other embodiments obtained by a person of ordinary skill in the art without any inventive work based on the embodiments in the present application are within the scope of protection of the present application. Embodiments of the present application will be described in detail below with reference to the drawings.
In a first aspect of the present application, a method for determining an equidistant great circle route, as shown in fig. 1, mainly includes:
step S1, determining the longitude and latitude of the starting point and the ending point of the great circle route;
step S2, calculating great circle route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram Luger projection;
step S3, calculating the distance between the starting point and the end point under the plane coordinates of the great circle route;
step S4, dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval, and calculating the plane coordinate of each interval point;
and step S5, converting the plane coordinates of each interval point into longitude and latitude by using a back calculation formula of Gaussian-gram Luger projection.
In some alternative embodiments, the set interval is 40-60 km.
In some alternative embodiments, the set interval is 50 km.
In some alternative embodiments, further comprising:
and S6, forming a great circle route according to the plurality of longitudes and latitudes calculated in the step S5, and guiding the aircraft to navigate.
The method mainly solves the problems that the longitude and the latitude of a starting point and a finishing point are given, the route is divided by a given interval distance, and the longitude and latitude coordinates of each interval inflection point are obtained so as to express a great circle route in a broken line mode.
In steps S1-S2, (1) from the longitude and latitude of the start point and the end point, the corresponding plane coordinates of the start point and the end point and the distance between the two points are calculated according to the forward calculation formula of "gaussian-gram-luger projection", as shown in table 1.
TABLE 1 longitude and latitude coordinates and ground coordinates correspondence table
The gaussian projection forward formula is as follows:
wherein the content of the first and second substances,
the arc length on the central meridian corresponding to the X-ellipsoid latitude B;
e-ellipsoid first eccentricity;
e' -ellipsoid second eccentricity;
a-the major axis radius of the ellipsoid;
the curvature radius of the N-ellipsoidal unitary fourth-element ring;
b-geodetic latitude;
l-geodetic longitude difference (geodetic longitude-central longitude);
t＝tan B；
η＝e'cos B。
then, the plane coordinates of each interval point are calculated according to the given interval distance, and in this embodiment, the interval distance is set to 50km as required, and the plane coordinates of the interval points are obtained, as shown in table 2.
TABLE 2 plane coordinates of each interval point
And finally, converting the plane coordinates of the interval points into longitude and latitude by using a back calculation formula of the Gaussian-gram Luger projection, and correspondingly outputting.
The inverse calculation formula of the gaussian projection coordinate is as follows:
the results are shown in Table 3.
TABLE 3 latitude and longitude of each interval point
The method and the device are not realized in the previous models, the problem that the projection of the traditional ink card holder is seriously deviated from a great circle route in a high latitude area is solved, the route is closer to a real earth great circle route, and the economic principle of remote navigation is met.
The method solves the problem that the calculation result is divergent when the calculation error is large and the starting point and the end point latitude are close in the existing method in the high latitude area, and is wider in applicability and changed in precision. The application range of the equidistant great circle route design is effectively expanded, and powerful technical support is provided for the design of the long-distance navigation route of the airplane.
The second aspect of the present application provides an equidistant great circle route determining device corresponding to the above method, including:
the starting longitude and latitude determining module is used for determining the longitude and latitude of a starting point and an ending point of the great circle route;
the starting plane coordinate calculation module is used for calculating large circular route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram-Luger projection;
the distance calculation module is used for calculating the distance between a starting point and a terminal point under the plane coordinates of the great circle route;
the interval division module is used for dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval and calculating the plane coordinate of each interval point;
and the interval point longitude and latitude determining module is used for converting the plane coordinates of each interval point into the longitude and latitude by using a back calculation formula of Gaussian-Kruger projection.
In some alternative embodiments, the set interval is 40-60 km.
In some alternative embodiments, the set interval is 50 km.
In some alternative embodiments, further comprising:
and the great circle route determining module is used for forming a great circle route according to the plurality of the longitudes and latitudes calculated by the interval point longitude and latitude determining module and guiding the aircraft to navigate.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (8)
1. A method for determining equidistant great circle route is characterized by comprising the following steps:
step S1, determining the longitude and latitude of the starting point and the ending point of the great circle route;
step S2, calculating great circle route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram Luger projection;
step S3, calculating the distance between the starting point and the end point under the plane coordinates of the great circle route;
step S4, dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval, and calculating the plane coordinate of each interval point;
and step S5, converting the plane coordinates of each interval point into longitude and latitude by using a back calculation formula of Gaussian-gram Luger projection.
2. The method for determining equidistant great circle route of claim 1, wherein the set interval is 40-60 km.
3. The method for determining equidistant great circle route of claim 2, wherein the set interval is 50 km.
4. The method for determining an equidistant great circle route as claimed in claim 1, further comprising:
and S6, forming a great circle route according to the plurality of longitudes and latitudes calculated in the step S5, and guiding the aircraft to navigate.
5. An equidistant great circle route determining device is characterized by comprising:
the starting longitude and latitude determining module is used for determining the longitude and latitude of a starting point and an ending point of the great circle route;
the starting plane coordinate calculation module is used for calculating large circular route plane coordinates corresponding to the starting point and the end point according to a forward calculation formula of Gaussian-gram-Luger projection;
the distance calculation module is used for calculating the distance between a starting point and a terminal point under the plane coordinates of the great circle route;
the interval division module is used for dividing the distance between the starting point and the end point under the plane coordinate of the great circle route according to a set interval and calculating the plane coordinate of each interval point;
and the interval point longitude and latitude determining module is used for converting the plane coordinates of each interval point into the longitude and latitude by using a back calculation formula of Gaussian-Kruger projection.
6. The equidistant great circle route determination device of claim 5, wherein the set interval is 40-60 km.
7. The equidistant great circle route determination device of claim 6, wherein the set interval is 50 km.
8. The equidistant great circle route determination device of claim 5, further comprising:
and the great circle route determining module is used for forming a great circle route according to the plurality of the longitudes and latitudes calculated by the interval point longitude and latitude determining module and guiding the aircraft to navigate.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114141058A (en) * | 2021-08-27 | 2022-03-04 | 张慎佳 | Synchronous coordinate numerical control navigation method for large circular navigation route |
| CN114415721A (en) * | 2021-12-29 | 2022-04-29 | 中国航空工业集团公司西安飞机设计研究所 | Method and device for rapidly judging whether aircraft has over-optimum arc |
| CN115880973A (en) * | 2023-02-02 | 2023-03-31 | 北京东方瑞丰航空技术有限公司 | Method, device and equipment for generating flight simulator view of pseudo-spherical coordinate system |
| WO2023138199A1 (en) * | 2022-01-21 | 2023-07-27 | 腾讯科技（深圳）有限公司 | Route drawing method and apparatus, computer device, storage medium and program product |
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